System, method, and computer program for creating geometry-compliant lattice structures

ABSTRACT

A system and method of creating a shape-conforming lattice structure for a part formed via additive manufacturing. The method includes receiving a computer model of the part and generating a finite element mesh. A lattice structure including a number of lattice cellular components may also be generated. Some of the mesh elements of the finite element mesh may be deformed so that the finite element mesh conforms to the overall shape of the part. The lattice structure may then be deformed so that the lattice structure has a cellular periodicity corresponding to the finite elements of the finite element mesh. In this way, the part retains the benefits of its overall shape and the benefits of lattice features without introducing structural weak points, directional stresses, and other structural deficiencies.

RELATED APPLICATIONS

This application is a continuation application, and claims prioritybenefit with regards to common subject matter, of non-provisional U.S.patent application Ser. No. 16/366,690, filed Mar. 27, 2019, entitledSYSTEM, METHOD, AND COMPUTER PROGRAM FOR CREATING GEOMETRY-COMPLIANTLATTICE STRUCTURES, issued as U.S. Pat. No. 10,642,253 on May 5, 2020.Application Ser. No. 16/366,690 claims priority benefit ofnon-provisional U.S. patent application Ser. No. 14/997,238, filed Jan.15, 2016, entitled SYSTEM, METHOD, AND COMPUTER PROGRAM FOR CREATINGGEOMETRY-COMPLIANT LATTICE STRUCTURES, issued as U.S. Pat. No.10,274,935 on Apr. 30, 2019. The above-referenced patent applicationsand patents are hereby incorporated by reference into the presentapplication in their entireties.

STATEMENT REGARDING FEDERALLY-SPONSORED RESEARCH OR DEVELOPMENT

This invention was made with Government support under Contract No.:DE-NA0000622 awarded by the United States Department of Energy/NationalNuclear Security Administration. The Government has certain rights inthe invention.

BACKGROUND

Additive manufacturing is often used for creating prototypes and unique,complex, and/or low-production parts. Such parts are often formed withlattice structures for improving structural rigidity withoutsignificantly increasing weight of the parts. However, these latticestructures are often truncated when overall shapes of the latticestructures do not match overall shapes of the parts. For example, anorthogonal lattice structure may be cropped to fit a part having acircular overall shape. Some of the cropped cellular components of theorthogonal lattice structure become structurally compromised as aresult, which may introduce undesired stress paths and stressconcentrations. Truncating and/or cropping cellular components may alsointroduce unwanted artifacts in the computer model of the part, whichmay complicate the additive manufacturing process.

SUMMARY OF THE INVENTION

Embodiments of the present invention solve the above-mentioned problemsand provide a distinct advance in the art of additive manufacturing.More particularly, the present invention provides a computer modelingand additive manufacturing system for creating a shape-conforminglattice structure of a part formed via additive manufacturing.

An embodiment of the present invention is a method of creating ashape-conforming lattice structure including receiving a computer modelof a part and generating a finite element mesh corresponding to anoverall shape of the part. A lattice structure including a number oflattice cellular components may also be generated. The lattice structuremay then be deformed so that the lattice structure has a cellularperiodicity corresponding to the mesh elements of the finite elementmesh. In this way, the part retains its overall shape and receives thebenefits of lattice features without introducing structural weak points,unintentional stress paths, and other structural deficiencies.

Another embodiment of the present invention is another method ofcreating a shape-conforming lattice structure including generating acomputer model of a part and generating a finite element meshcorresponding to the computer model of the part. A lattice structureincluding a number of lattice cellular components may also be generated.The mesh elements of the finite element mesh may be free-form deformedso that the finite element mesh conforms to the overall shape of thepart. The lattice structure may then be deformed so that the latticestructure has a cellular periodicity corresponding to the mesh elementsof the finite element mesh. Each individual mesh element, when all meshgeneration and modification is complete, may be independent from allother mesh elements in the finite element mesh. This enables parallelprocessing of the deformed lattice structure. In some embodiments, eachindividual mesh element could be assigned a reduced-order model based onits deformed lattice structure which may reduce a later simulation ofthe entire part.

This summary is provided to introduce a selection of concepts in asimplified form that are further described below in the detaileddescription. This summary is not intended to identify key features oressential features of the claimed subject matter, nor is it intended tobe used to limit the scope of the claimed subject matter. Other aspectsand advantages of the present invention will be apparent from thefollowing detailed description of the embodiments and the accompanyingdrawing figures.

BRIEF DESCRIPTION OF THE DRAWING FIGURES

Embodiments of the present invention are described in detail below withreference to the attached drawing figures, wherein:

FIG. 1 is a perspective view of a computer modeling and additivemanufacturing system constructed in accordance with an embodiment of thepresent invention;

FIG. 2 is a schematic view of the computer modeling system of FIG. 1;

FIG. 3 is a perspective view of the additive manufacturing system ofFIG. 1;

FIG. 4 is a perspective view of an overall shape of a part modeled viathe computer modeling system of FIG. 1;

FIG. 5 is an elevational cutaway view of the overall shape of FIG. 4;

FIG. 6 is a finite element mesh of the overall shape of the part of FIG.4;

FIG. 7 is an elevational cutaway view of the finite element mesh of FIG.6;

FIG. 8 is a perspective view of a lattice cellular component within amesh element;

FIG. 9 is a perspective view of the lattice cellular component of FIG. 8being deformed;

FIG. 10 is a top view of the part having a lattice structure based onthe lattice cellular component of FIG. 8;

FIG. 11 is an elevational partial cutaway view of the lattice structureof FIG. 10;

FIG. 12 is a flow diagram of a method of creating a part design via thecomputer modeling system of FIG. 2; and

FIG. 13 is a flow diagram of a method of forming the part of FIG. 10 viathe additive manufacturing system of FIG. 3.

The drawing figures do not limit the present invention to the specificembodiments disclosed and described herein. The drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of the invention.

DETAILED DESCRIPTION OF THE EMBODIMENTS

The following detailed description of the invention references theaccompanying drawings that illustrate specific embodiments in which theinvention can be practiced. The embodiments are intended to describeaspects of the invention in sufficient detail to enable those skilled inthe art to practice the invention. Other embodiments can be utilized andchanges can be made without departing from the scope of the presentinvention. The following detailed description is, therefore, not to betaken in a limiting sense. The scope of the present invention is definedonly by the appended claims, along with the full scope of equivalents towhich such claims are entitled.

In this description, references to “one embodiment”, “an embodiment”, or“embodiments” mean that the feature or features being referred to areincluded in at least one embodiment of the technology. Separatereferences to “one embodiment”, “an embodiment”, or “embodiments” inthis description do not necessarily refer to the same embodiment and arealso not mutually exclusive unless so stated and/or except as will bereadily apparent to those skilled in the art from the description. Forexample, a feature, structure, act, etc. described in one embodiment mayalso be included in other embodiments, but is not necessarily included.Thus, the current technology can include a variety of combinationsand/or integrations of the embodiments described herein.

Turning to the drawing figures, and particularly FIGS. 1-3, a computermodeling and additive manufacturing system 10 constructed in accordancewith an embodiment of the present invention is illustrated. The computermodeling and additive manufacturing system 10 broadly comprises acomputer aided design (CAD) system 12 and an additive manufacturingsystem 14.

The CAD system 12 may be used for designing and generating a computermodel of a part 100 and broadly includes a processor 16, a memory 18, atransceiver 20, a plurality of inputs 22, and a display 24. The CADsystem 12 may be integral with or separate from the additivemanufacturing system 14.

The processor 16 generates the computer model of the part 100 accordingto inputs and data received from a user. The processor 16 may include acircuit board, memory, display, inputs, and/or other electroniccomponents such as a transceiver or external connection forcommunicating with external computers and the like.

The processor 16 may implement aspects of the present invention with oneor more computer programs stored in or on computer-readable mediumresiding on or accessible by the processor. Each computer programpreferably comprises an ordered listing of executable instructions forimplementing logical functions in the processor 16. Each computerprogram can be embodied in any non-transitory computer-readable medium,such as the memory 18 (described below), for use by or in connectionwith an instruction execution system, apparatus, or device, such as acomputer-based system, processor-containing system, or other system thatcan fetch the instructions from the instruction execution system,apparatus, or device, and execute the instructions.

The memory 18 may be any computer-readable non-transitory medium thatcan store the program for use by or in connection with the instructionexecution system, apparatus, or device. The computer-readable medium canbe, for example, but not limited to, an electronic, magnetic, optical,electro-magnetic, infrared, or semi-conductor system, apparatus, ordevice. More specific, although not inclusive, examples of thecomputer-readable medium would include the following: an electricalconnection having one or more wires, a portable computer diskette, arandom access memory (RAM), a read-only memory (ROM), an erasable,programmable, read-only memory (EPROM or Flash memory), an opticalfiber, and a portable compact disk read-only memory (CDROM).

The transceiver 20 may transmit data and instructions between the CADsystem 12 and the additive manufacturing system 14 over a wirelesscommunication network. Alternatively, a wired or integrated setup may beused between the CAD system 12 and the additive manufacturing system 14.

The inputs 22 allow a user to design and modify a model of the part 100and may comprise a keyboard, mouse, trackball, touchscreen, buttons,dials, virtual inputs, and/or a virtual reality simulator. The inputs 22may also be used to control or instruct the additive manufacturingsystem 14.

The display 24 may display a two-dimensional or three-dimensionalrepresentation of the model and may also display model data, computeroptions, and other information via a graphical user interface (GUI). Thedisplay 24 may be separate from or integrated with the additivemanufacturing system 14.

The additive manufacturing system 14 produces prototypes and parts suchas part 100 and broadly includes a frame 26, a support surface 28, amaterial reserve 30, a feeder 32, a material applicator 34, a set ofmotors 36, and a processor 38. The additive manufacturing system 14 maybe integral with or separate from the powder coating system 14.

The frame 26 provides structure for the support surface 28, materialreserve 30, feeder 32, material applicator 34, motors 36, and/or theprocessor 38 and may include a base, vertical members, cross members,and mounting points for mounting the above components thereto.Alternatively, the frame 26 may be a walled housing or similarstructure.

The support surface 28 supports the part 100 as it is being constructedand may be a stationary or movable flat tray or bed, a substrate, amandrel, a wheel, scaffolding, or similar support. The support surface28 may be integral with the additive manufacturing system 14 or may beremovable and transferable with the part 100 as the part 100 is beingconstructed.

The material reserve 30 retains additive manufacturing material 40 andmay be a hopper, tank, cartridge, container, spool, or other similarmaterial holder. The material reserve may be integral with the additivemanufacturing system 14 or may be disposable and/or reusable.

The additive manufacturing material 40 may be used for forming part 100and may be in pellet or powder form, filament or spooled form, or anyother suitable form. The additive manufacturing material 40 may be anyplastic, polymer, or organic material suitable for use in additivemanufacturing. For example, the additive manufacturing material 40 maybe acrylonitrile butadiene styrene (ABS), polyamide, straw-basedplastic, or other similar material.

The feeder 32 directs the additive manufacturing material 40 to thematerial applicator 34 and may be a spool feeder, a pump, an auger, orany other suitable feeder. Alternatively, the additive manufacturingmaterial 40 may be gravity fed to the material applicator 34.

The material applicator 34 deposits the additive manufacturing material40 onto the support surface 28 and previously constructed layers. Thematerial applicator 34 may include a nozzle, guide, sprayer, or othersimilar component for channeling the additive manufacturing material 40and a laser, heater, or similar component for melting the additivemanufacturing material and bonding (e.g., sintering) the additivemanufacturing material 40 onto a previously constructed layer. Thematerial applicator 34 may be sized according to the size of thepellets, powder, or filament being deposited.

The motors 36 position the material applicator 34 over the supportsurface 28 and previously constructed layers and move the materialapplicator 34 as the additive manufacturing material is deposited ontothe support surface 28 and the previously constructed layers. The motors36 may be oriented orthogonally to each other so that a first one of themotors 36 is configured to move the material applicator 34 in a lateral“x” direction, a second one of the motors 36 is configured to move thematerial applicator 34 in a longitudinal “y” direction, and a third oneof the motors 36 is configured to move the material applicator 34 in analtitudinal “z” direction. Alternatively, the motors 36 may move thesupport surface 28 (and hence the part 100) while the materialapplicator 34 remains stationary.

The processor 38 directs the material applicator 34 via the motors 36and activates the material applicator 34 such that the materialapplicator 34 deposits the additive manufacturing material 40 onto thesupport surface 28 and previously constructed layers according to acomputer aided design of the part. The processor 38 may include acircuit board, memory, display, inputs, and/or other electroniccomponents such as a transceiver or external connection forcommunicating with the processor 16 of the CAD system 12 and otherexternal computers. It will be understood that the processor 38 may beone and the same as processor 16 of the CAD system 12.

The processor 38 may implement aspects of the present invention with oneor more computer programs stored in or on computer-readable mediumresiding on or accessible by the processor. Each computer programpreferably comprises an ordered listing of executable instructions forimplementing logical functions in the processor 38. Each computerprogram can be embodied in any non-transitory computer-readable mediumfor use by or in connection with an instruction execution system,apparatus, or device, such as a computer-based system,processor-containing system, or other system that can fetch theinstructions from the instruction execution system, apparatus, ordevice, and execute the instructions. In the context of thisapplication, a “computer-readable medium” can be any non-transitorymeans that can store the program for use by or in connection with theinstruction execution system, apparatus, or device. Thecomputer-readable medium can be, for example, but not limited to, anelectronic, magnetic, optical, electro-magnetic, infrared, orsemi-conductor system, apparatus, or device. More specific, although notinclusive, examples of the computer-readable medium would include thefollowing: an electrical connection having one or more wires, a portablecomputer diskette, a random access memory (RAM), a read-only memory(ROM), an erasable, programmable, read-only memory (EPROM or Flashmemory), an optical fiber, and a portable compact disk read-only memory(CDROM).

It will be understood that the additive manufacturing system 14 may beany type of additive manufacturing or “3D printing” system such as asintering, laser melting, laser sintering, extruding, fusing,stereolithography, extrusion, light polymerizing, powder bed, wireadditive, or laminated object manufacturing system. The additivemanufacturing system 14 may also be a hybrid system that combinesadditive manufacturing with molding, scaffolding, and/or othersubtractive manufacturing or assembly techniques.

Turning to FIGS. 12 and 13, and with reference to FIGS. 4-11, use of thecomputer modeling and additive manufacturing system 10 for creating acomputer model of the part 100 and forming the part 100 via additivemanufacturing according to the computer model will now be described inmore detail. First, a computer-aided model may be created (or receivedfrom another computer system), in which an overall shape 102 of the part100 (FIG. 4) may be generated, as shown in block 200 of FIG. 12. Thismay be a wire-frame model, surface model, solid model, or any othersuitable CAD model that defines or exhibits the overall shape 102 of thepart 100.

The overall shape 102 of the part 100 may optionally be divided into twoor more sections 104 a,b (FIG. 5), as shown in block 202. One or more ofthe sections 104 a,b may encompass a portion of the part 100 that willonly be subjected to basic lattice deformations. For example, section104 b may include lattice cellular components that that will be deformedonly via basic lattice deformations such as translation, rotation,and/or isotropic, orthotropic, and anisotropic scaling to form the lowerportion of the part. This may reduce or simplify calculations andrendering performed by the CAD system 12.

A finite element mesh 106 (shown fully deformed in FIGS. 6 and 7) maythen be created, as shown in block 204. The finite element mesh 106 mayinclude a plurality of mesh elements 108 each representing a deformableunit. Each mesh element 108 may have a number of corner nodes 110, anumber of edge midpoint nodes 112, face midpoint nodes, volume midpointnodes, and/or any other nodes forming the basis of mesh element 108manipulation and deformation. For example, an 8-node hex will havecorner nodes. A 20-node hex will have corner nodes and edge midpointnodes. A 27-node hex will have corner nodes, edge midpoint nodes, facemidpoint nodes, and a volume midpoint nodes. The finite element mesh 106may be a first order, second order, or higher order finite element mesh106 and may be triagonal, quadrilateral, tetrahedral, pyramidal,hexahedral, dodecahedral, or other polyhedral sub-volume shapes. Thefinite element mesh 106 thus includes sub-volumes (mesh elements 108)that provide spatial coordinates, as defined by the nodes fordeformation processing. Higher order mesh elements 108 can be used forhigher order interpolation. Interpolation can be a free-formdeformation, an isogeometric shape function, or an isoparametric shapefunction. The finite element mesh 106 may include mesh elements of twoor more base shapes. The finite element mesh 106 may be created toconform to and be compliant with the overall shape of the part (FIGS. 6and 7). However, the finite element mesh 106 may undergo additionaldeformation, as described below.

The finite element mesh 106 may optionally undergo smoothing, Jacobianoptimization, Laplace optimization, regularity optimization, or otherdeformations, as shown in block 206. The finite element mesh 106 mayalso be manually deformed or edited.

A lattice cellular component 114 (FIGS. 8 and 9) may then be created, asshown in block 208. The lattice cellular component 114 may be arepeatable structural unit for populating the lattice structure(described below) and may itself be a wire-frame model, surface model,solid model, or any other suitable CAD model. The lattice cellularcomponent 114 may have a shape that coincides with the shape of the meshelements 108 of the finite element mesh 106. For example, if the finiteelement mesh 106 is quadrilateral, the lattice cellular component 114may also be quadrilateral and may extend to boundaries and/or nodes of anon-deformed mesh element 108. The lattice cellular component 114 mayinclude truss members, cross members, frame-like members, or any otherstructural components and may have chamfers, fillets, recesses, arches,and complex curves. The lattice cellular component 114 may also includethrough-holes, channels, voids, chambers, and other negative spaces suchthat the resulting lattice structure is strong yet lightweight. Thisconstruction also simplifies and improves deformation of the latticestructure, as described below. The lattice cellular component 114 may behoneycomb shaped, cube shaped, tube shaped, or any other suitable baseshape.

A lattice structure 116 (shown fully deformed in FIGS. 10 and 11) basedon the lattice cellular component 114 may then be generated, as shown inblock 210. Each component in the lattice structure 116 may correspond toa mesh element 108 of the finite element mesh 106. The lattice structure116 may be a matrix, array, or network of repetitions or copies of thelattice cellular component 114. The lattice structure 116 may include ahoneycomb pattern, tube pattern, cube pattern, or any other pattern. Thepattern may extend along one or more axes. In some embodiments, thelattice structure 116 may include lattice cellular components of two ormore different base shapes.

The lattice structure 116 may then be modified to conform to thedeformed finite element mesh 106 such that the lattice structure 116 hasa cellular periodicity corresponding to the mesh elements 108 of thefinite element mesh 106, as shown in block 212. In this way, the latticestructure 116 conforms to the overall shape 102 of the part 100. In oneembodiment, the lattice structure 116 may be sampled at various pointsalong its surface or within its volume. The surface may be faceted,where each facet may be a polygon including vertices and edges. Thisfaceted form may be stored as a stereolithography (STL) file, Polygonfile (PLY) file, Additive Manufacturing file (AMF), or as a finiteelement mesh. The vertices then provide spatial coordinates forevaluating the deformed mesh elements 108 or lattice cellular components114. Deformation of each lattice cellular component 114 may includerotation and translation, in addition to stretching and skewing. Thatis, a lattice cellular component may undergo global deformation withoutundergoing local deformation. Note that the part 100 may essentially bethe above lattice structure 116 or may include a shell, housing, outerwall, mounting bosses, and other major features in addition to thelattice structure 116.

Turning to FIG. 13, and with reference to FIG. 3, the part 100 may thenbe created via the additive manufacturing system 14. First, the additivemanufacturing material may be inserted in or positioned on the materialreserve 20 of the additive manufacturing system 14, as shown in block300. For example, a spool of the additive manufacturing material 40 maybe loaded onto the additive manufacturing system 14.

The additive manufacturing material 40 may then be deposited onto thesupport surface 28 via the material applicator 34 in successive layersaccording to the computer-aided design of the part 100, as shown inblock 302. To that end, activation of horizontally oriented motors invarious amounts allows for diagonal movement and curved movement of thematerial applicator 34. Activation of a vertically oriented motor may beused for relocating the material applicator 34 without depositingmaterial and/or raising the material applicator 34 for creation of a newlayer (see motors 36, above).

It will be understood that the above-described steps may be performed inany order, including simultaneously. In addition, some of the steps maybe repeated, duplicated, and/or omitted without departing from the scopeof the present invention.

The above-described computer modeling and additive manufacturing system10 and method provide several advantages over conventional systems. Forexample, features of the lattice structure 116 are not cut orcompromised to form the overall shape 102 of the part 100. Thiseliminates structural weak points, stress concentrations, andinefficient or imperfect structural properties. For example, an axiallysymmetric part would be expected to have axially symmetric structuralproperties. However, if the axially symmetric part is formed of anorthogonal lattice structure, stress concentrations will form where theorthogonal lattice structure is truncated to form the overall shape ofthe axially symmetric part. The computer modeling and additivemanufacturing system 10 eliminates this problem. The arrangement, size,and shape distribution of the lattice cellular components 114 may alsobe modified. Each mesh element 108 of the finite element mesh 106 may berecognized as a valid mesh element 108 by the software. As such, thephysical properties of each modified lattice cellular component 114 canbe used to apply a reduced-order model to the parent mesh elements 108of the modified lattice cellular components 114 so as to reduce thecomputational complexity of a subsequent simulation. The CAD system 12may also be used for analyzing and iteratively improving and optimizingthe lattice structure 116.

Although the invention has been described with reference to theembodiments illustrated in the attached drawing figures, it is notedthat equivalents may be employed and substitutions made herein withoutdeparting from the scope of the invention as recited in the claims.

Having thus described various embodiments of the invention, what isclaimed as new and desired to be protected by Letters Patent includesthe following:
 1. A method of creating a lattice structure for a partformed via additive manufacturing, the method comprising the steps of:generating a finite element mesh corresponding to an overall shape ofthe part via a processor, the finite element mesh having a plurality ofmesh elements, at least some of the plurality of mesh elements being atleast second order; generating a lattice cellular component via theprocessor, the lattice cellular component corresponding to a meshelement of the finite element mesh; generating a lattice structure basedon the lattice cellular component via the processor; and deforming thelattice structure via the processor such that the lattice structure hasa cellular periodicity corresponding to at least some of the pluralityof mesh elements of the finite element mesh so that the latticestructure conforms to the overall shape of the part.
 2. The method ofclaim 1, further comprising a step of interpolating at least some of theplurality of mesh elements.
 3. The method of claim 2, wherein the stepof interpolating the at least some of the plurality of mesh elementsincludes free-form deformation.
 4. The method of claim 2, wherein thestep of interpolating the at least some of the plurality of meshelements includes isogeometric shape function interpolation.
 5. Themethod of claim 2, wherein the step of interpolating the at least someof the plurality of mesh elements includes isoparametric shape functioninterpolation.
 6. The method of claim 1, further comprising a step ofsmoothing at least some of the plurality of mesh elements.
 7. The methodof claim 1, further comprising a step of applying Jacobian optimizationto at least some of the plurality of mesh elements.
 8. The method ofclaim 1, further comprising a step of applying Laplace optimization toat least some of the plurality of mesh elements.
 9. The method of claim1, further comprising a step of applying regularity optimization to atleast some of the plurality of mesh elements.
 10. The method of claim 1,further comprising a step of manually deforming at least some of theplurality of mesh elements.
 11. The method of claim 1, furthercomprising a step of free-form deforming at least some of the pluralityof mesh elements.
 12. The method of claim 1, wherein each finite elementof the plurality of mesh elements includes a plurality of nodes, thestep of conforming the lattice structure to the overall shape of thepart further including shifting at least some nodes of the plurality ofnodes.
 13. The method of claim 12, wherein the at least some of theplurality of mesh elements are 27-node hexes.
 14. The method of claim 1,wherein the at least some of the plurality of mesh elements aregreater-than-second-order mesh elements.
 15. The method of claim 1,wherein the plurality of mesh elements include mesh elements having atleast two different base shapes.
 16. A system for creating a part viaadditive manufacturing, the system comprising: a computer modelingsystem comprising: a processor configured to: generate a finite elementmesh corresponding to an overall shape of the part, the finite elementmesh having a plurality of mesh elements, at least some of the pluralityof mesh elements being at least second order; generate a latticecellular component according to inputs received from the user, thelattice cellular component corresponding to a mesh element of the finiteelement mesh; generate a lattice structure based on the lattice cellularcomponent; and deform the lattice structure such that the latticestructure has a cellular periodicity corresponding to the mesh elementsof the finite element mesh so that the lattice structure conforms to theoverall shape of the part.
 17. The system of claim 16, the processorbeing configured to apply Jacobian optimization to the at least some ofthe plurality of mesh elements.
 18. The system of claim 16, theprocessor being configured to apply Laplace optimization to the at leastsome of the plurality of mesh elements.
 19. The system of claim 16, theprocessor being configured to apply regularity optimization to the atleast some of the plurality of mesh elements.
 20. A method of creating alattice structure for a part formed via additive manufacturing, themethod comprising the steps of: dividing a computer model of the partinto at least two sections via a processor, the computer model having anoverall shape; generating a hexahedron finite element mesh correspondingto the at least two sections of the computer model of the part via theprocessor, the hexahedron finite element mesh having a plurality of meshelements, at least some of the plurality of mesh elements being at leastsecond order; generating a lattice cellular component via the processor,the lattice cellular component corresponding to a mesh element of thehexahedron finite element mesh; generating a lattice structure based onthe lattice cellular component via the processor; interpolating at leastsome of the mesh elements of the hexahedron finite element mesh in oneof the two sections according to at least one of free-form deformation,an isogeometric shape function, and an isoparametric shape function viathe processor such that the hexahedron finite element mesh conforms tothe overall shape of the part; optimizing at least some of the meshelements of the hexahedron finite element mesh in one of the twosections according to at least one of Jacobian optimization, Laplaceoptimization, and regularity optimization via the processor; anddeforming the lattice structure via the processor such that the latticestructure has a cellular periodicity corresponding to the mesh elementsof the hexahedron finite element mesh so that the lattice structureconforms to the overall shape of the part.